When I start my computer, there is this loud whirring noise like a plane engine. I usually lasts for about 10 seconds or so. It has never done this before I installed the graphics card so I am pretty sure it is the graphics card.
Asus Radeon HD 5670 (dust proof fan
Intel core i5 2400 stock cooler
OCZ modXstream Pro 500W

these are the only components with fans, and i only have one case fan. I've only had this rig for 2 weeks.

It is not unheard of for a GFX card's fan, and sometimes even CPU fan to ramp up to 100% immediately after power is applied. As long as it is still running afterwards and changing speed as needed, everything is fine.